Preheat oven to 375. Peel and dice the squash into small cubes. On a baking sheet, add squash and seasonings, drizzle with olive oil, and toss. Bake for about 45 minutes until golden and soft.
On another sheet baking sheet, toast the walnuts for a few minutes in the oven, until they smell nutty, set aside.
Bring avocado oil to high heat, slice the shallot and fry in the hot oil until golden/dark brown. Remove onto a paper towel to drain off the oil and cool. Save the oil.
In a blender, add 1/4 olive oil, the cooled shallot oil, champagne vinegar, the walnuts, Dijon, salt and pepper. Blend until smooth. If too stiff, add tablespoons of water until it loosens to desired consistency.
